Ellipsoidal Plasma Mirror Focusing of High Power Laser Pulses to
R. Wilson,1 M. King,1 R. J. Gray,1 D. C. Carroll,2 R. J. Dance,1 C. Armstrong,1, 2 S. J. Hawkes,2 R. J. Clarke,2 D. J. Robertson,3 D. Neely,2, 1 and P. McKenna1,∗ 1SUPA Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK 2Central Laser Facility, STFC Rutherford Appleton Laboratory, Oxfordshire OX11 0QX, UK
3Department of Physics, Durham University,
South Road, Durham DH1 3LE, UK
The design and development of an ellipsoidal F/1 focusing plasma mirror capable of increasing
the peak intensity achievable on petawatt level laser systems to >1022 Wcm−2 is presented. A
factor of 2.5 reduction in the focal spot size is achieved when compared to F/3 focusing with
a conventional (solid state) optic. We find a factor 3.6 enhancement in peak intensity, taking
into account changes in plasma mirror reflectivity and focal spot quality. The sensitivity of the
focusing plasma optic to misalignment is also investigated. It is demonstrated that an increase
in peak laser intensity from 3×1020Wcm−2to 1021Wcm−2results in a factor of two increase in
the maximum energy of sheath-accelerated protons from a thin foil positioned at the focus of the
intense laser light.
Throughout the history of high-power laser-plasma science new avenues of research have been enabled by increasing the peak laser intensity achievable. These include laser-driven particle acceleration [1,2], radiation sources [3, 4], relativistic optics [5,6], lab-oratory astrophysics [7,8] and warm dense matter [9,10]. Peak intensities in the range 1020−1021 Wcm−2 are now available at hundred-terawatt-to-petawatt-scale laser facili-ties. In a few years multi-petawatt laser systems such as APOLLON  and the extreme light infrastructure (ELI)  facilities will start operation. These lasers are expected to achieve focused intensities in the range 1022−1023Wcm−2, which will enable the explo-ration of ultra-intense laser-plasma phenomena, such as high-field quantum electrody-namics (QED) [13,14].
The typical approach adopted to increasing peak intensity involves increasing the laser pulse energy or decreasing its duration. When using conventional solid state optics, these approaches typically require an increase in the beam diameter to keep the energy density on the optic below the damage threshold. Alternatively, the focal spot size can be decreased, by implementing a small F-number (F/#) focusing optic (large numerical aperture). Such optics are typically expensive and are susceptible to damage from target debris due to their short focal length (and thus close proximity to the target).
the main pulse are below the threshold intensity required to ionise the medium and are therefore transmitted through it. In this way the main pulse which is reflected from the plasma has a sharper rising edge and higher intensity contrast (ratio of the peak intensity to the intensity of the ASE pedestal). PPMs have been used in this way to enable experimentation with ultra-thin target foils, resulting in the development of new ion acceleration  and high-harmonic generation [19,20] mechanisms. In addition, there have been several dedicated studies undertaken to understand and characterise these important optical components [21–24].
The fact that light is reflected from a thin plasma layer formed on the substrate sur-face means that the sursur-face can be curved to induce focusing (just as in conventional solid state optics). By appropriate choice of the surface curvature, an incident focusing laser beam can be made to focus with an even smaller F/#. A focusing plasma mirror (FPM) of ellipsoidal geometry with two foci, such that demagnification of a focal spot occurs from one focal position to the other, satisfies the need to have off-axis focusing to ensure that the target is not blocking the incoming laser beam. Such an optic is attractive not only because of the increase in peak laser intensity achievable, but also because it improves pulse intensity contrast in the same way as a PPM. The use of such an optic was first demonstrated in a proof-of-principle experiment on a terawatt (TW) level laser system reported by Konet al and Nakatsutsumiet al , whereby a F/0.4 FPM was devel-oped and achieved a five-fold reduction in focal spot size compared to the spot formed by a conventional F/2.7 off-axis parabolic (OAP) mirror. The intensity enhancement was in-directly diagnosed by measurement of the maximum energy of protons accelerated from a thin target foil positioned at the FPM beam focus.
PRINCIPLES OF DESIGN AND OPERATION
As in the case of the previously trialled FPM [25, 26], an ellipsoidal geometry was chosen to induce the plasma mirror focusing, as depicted in Fig. 1(b). This shape has two foci positions, f1 and f2, located along the major axis, equidistant from the centre. This enables point-to-point (i.e. focus-to-focus) imaging. Depending on the degree of elliptical eccentricity,e, a reduction or enlargement in the image size at one focus can be obtained when an object is placed at the other, i.e. the magnification of the optic. The magnification is equal to the ratio of lengthsβ/α, whereαis defined as the distance from f1 to a point on the mirror surface andβ is defined as the distance from the same point to f2. The ratio changes as a function of the beam incident angle,θin, with respect to the major axis and can therefore be expressed as :
m= (1 +e
where the eccentricity is given by e = p(1−b2/a2); a and b being the semi-major and semi-minor axis length, respectively.
In practical terms, a conventional OAP can be aligned such that the focus coincides with f1of the FPM. As the light diverges beyond f1it reflects from the plasma it forms on the curved optic surface and is imaged to position f2. The focal spot at f1 is demagnified at f2 depending on the chosen geometry of the FPM and the angleθin.
Laser From OAP θin
Focusing Plasma Mirror
10 mm 300 mm
Planar Plasma Mirror
Laser From OAP
Figure 1: Schematic diagrams showing: (a) the overall optical set up in the Vulcan target chamber; (b) the
operation of the ellipsoidal focusing plasma mirror, where the incoming laser is focused by a conventional
OAP to position f1 and the FPM focuses the beam to position f2, with magnification given by β/α; (c)
the operation of a reference planar plasma mirror. (d)-(e) Photographs of the manufactured FPM optic
showing: (d) the front surface; and (e) a side view, demonstrating the ellipsoidal structure. The fiducial
markers highlighted are used for alignment of the optic.
within the FWHM focal spot).
The dimensions of the FPM depends on the desired energy reflectivity of the optic and thus the incident laser intensity on the optic surface (the reflectivity dependence on laser intensity is discussed in references [22,24]). A region of high specular reflectivity (∼70%), is established at an incident intensity of∼1015Wcm−2, as shown in Fig. 2. The laser intensity at the optic surface is determined by the distance the beam expands from f1 to the surface, i.e. α in Fig. 1(b). Through consideration of Gaussian beam expan-sion, this distance can be determined such that an intensity of 1015 Wcm−2 is achieved, resulting in a high optical reflectivity. For alignment purposes, the incidence angleθin is selected to be 19.4° for this optimal intensity, along with a selected minimum distance of the focus f2 from the ellipsoidal surface for practical target placement. Using these parameters, the remaining values required to define the shape of the optic are obtained using simple trigonometric expressions describing an ellipse.
To validate the design before manufacture, analytical modelling was conducted using optical ray-tracing software (Zemax). Figure3(a)-(b) shows the results for the input focal spot and the resultant output focus formed by the FPM. This produces a demagnification of×2.9, based on input and output focal spots of 1.71µm and 0.59µm (FWHM), respec-tively. This modelling was conducted using 532 nm light to enable direct comparison with experimental tests discussed in the next section.
be (4.2±0.3)%, and thus for the predicted plasma reflectivity of ∼70% the optic is ex-pected to increase the intensity contrast by a factor of 16.7; approximately an order of magnitude less than an AR coated plasma mirror.
To characterise the plasma reflectivity of the selected FPM substrate material, the Vul-can PW laser was used to investigate the reflectivity of a PPM, made from the same transparent PMMA material, as a function of incident laser intensity. The sample was irradiated with p-polarized pulses, at a 35° incident angle relative to the mirror surface (the same as the operational incident angle of the FPM design). The laser intensity was varied by changing the distance between the optic surface and the laser focus, at which a maximum intensity of approximately∼1016 Wcm−2 is achieved using ∼0.25 J pulses. The energy of the incident and reflected light was measured using a Gentec pyroelectric energy meter for absolute calorimetry. The specular reflectivity as a function of incident laser intensity is shown in Fig.2.
PMMA (Reduced Energy Shots) Silica Glass (Full Energy Shot) PMMA (Full Energy Shot) Reference Data (Dromey et al)
1012 1013 1014 1015 1016 1017
0 10 20 30 40 50 60 70 80 S pe cu la rR ef le ct ed E ne rg y Fr ac tio n (% )
Incident Intensity (Wcm-2)
Figure 2: Percentage of laser light specularly reflected from the plasma mirror as a function of the laser
intensity at the plasma mirror surface. Red data points are results from reduced energy Vulcan PW pulses
on a flat PMMA sample and the grey points correspond to reference data from Dromeyet al for a 500
fs pulse and a fused silica PPM, with 6° laser incidence angle. A quadratic fit is made to this data between
incident intensity of 1013−1016Wcm−2, as illustrated by the dotted green curve. The blue and purple data
points represent full energy shots on flat samples of silica glass and PMMA, respectively. Each data point
represents a single laser shot.
An experimental set-up utilising a low-power continuous wave (CW) laser was devel-oped to characterise the manufactured FPM design. This enabled the focal spot reduc-tion to be quantified and the feasibility of the use of each optic for laser-target interacreduc-tion studies to be tested. The set-up was not only used for the focal spot characterisation but was also used to pre-align the optics prior to use on the Vulcan PW laser system. In this low-power illumination mode, the substrate is not ionised and thus the optic simply functions as a conventional partially-reflecting solid-state optic.
for optic testing as it is much lower than the normal operational wavelength (1053 nm), and thus will aid in determining if there are any unwanted irregularities in the optic’s focusing, which are displayed more prominently with lower wavelengths. To measure the focal spot formed by both the OAP and FPM, an infinity-corrected microscope objec-tive (×50 and N.A.=0.42) was used to image the spot to a CCD camera. For alignment and imaging purposes both the optic and camera set-up were mounted on micrometer controlledxyz-translation stages, where thez-axis of the FPM motion was set along the direction of the OAP input beam.
Characterisation of the optic was conducted by analysing the output focal spot formed by the FPM under optimum alignment, occurring when the OAP input focus spatially coincides with the FPM focus, f1. An example result of these are displayed in Fig. 3 (c)-(d).
The optic testing established that the typical output focal spot formed by the FPM (at f2), displayed in Fig. 3(d), is 0.76µm (FWHM), with 28.3% energy encircled within the FWHM diameter. As the input focal spot, shown in Fig. 3(c), was 1.91µm (FWHM) with 35.1% FWHM encircled energy, a focal spot demagnification of ×2.51 is achieved. The reduction in encircled energy may be attributed to small optic misalignments, or inherent deviations in the optics shape from optimal design. It should be noted that this encircled energy is larger than the FPM fielded in the first proof-of-principle experiment  for which 17% is reported. Both experiment and ray-tracing results are in good agreement with the theoretically predicted demagnification of×3 for the design.
Using the above characterisation results, the expected enhancement factor in the laser intensity, IEnh, under plasma operation can be calculated. This parameter depends on the input (φin) and output (φout) spot sizes, FWHM encircled energies (Ein and Eout, respectively), and the plasma optic reflectivity (Γp), as follows:
IEnh= (φin/φout)2·Γp·(Eout/Ein) (2)
Normalised Counts 0 0.2 0.4 0.6 0.8 1 Y ( µ m) −4 −3 −2 −1 0 1 2 3 4
Input Focal Spot Output Focal Spot
(a) (b) (c) (d) Testing Set-up ( λ = 532 nm) Ray-Trace ( λ = 532 nm) Y ( µ m) −4 −3 −2 −1 0 1 2 3 4
Vulcan PW Laser
( λ = 1053 nm ) −10 −5 0 5 10 Y ( µ m)
−10 −5 0 5 10
X (µm) −10 −5 X (µm)0 5 10
Normalised Counts 0 0.2 0.4 0.6 0.8 1 (e) (f)
−4 −3 −2 −1 0 1 2 3 4 −4 −3 −2 −1 0 1 2 3 4
X (µm) X (µµm)
Figure 3: (a)-(b) Calculated laser focal spot distributions at (a) f1and (b) f2from Zemax ray trace modelling
of the FPM operation. (c)-(d) corresponding measured spatial-intensity distributions using the
characteri-sation set-up (with 532 nm light). (e)-(f) corresponding measured focal spot distributions using the Vulcan
PW laser, with low power (CW operation) 1053 nm light.
Sensitivity to Misalignment
Successful FPM operation depends strongly upon achieving optimised alignment, as presented in Fig. 3, which is reliant upon the OAP focus spatially coinciding with f1, thus accurate optic positioning. Exploring the effect of misalignment is important to test the feasibility of these optics. Variations in the OAP focus position can occur on the micron scale on high power laser systems due to various effects, including thermal lensing in the laser chain which can alter the divergence of the incoming pulse prior to focusing. The testing set-up was used to implement a controlled displacement in the OAP focus position, relative to f1, for the three possible displacement directions,∆x,∆y and∆z. Figure4(a)-(b) shows the effect on the output focus quality for varying degrees of misalignment. This is quantified by measuring the percentage of focal spot energy contained within a circle of diameter equal to the FWHM of the optimised focus (Fig. 3(d)).
It is evident from Fig. 4(a) that displacements in∆xand∆yresult in the quality of the output focus being degraded. Results indicate that intensity enhancement with the FPM can only be achieved for displacements of<10 µm, for misalignments in only one axis (∆xor∆y). Above this value, and in misalignments of both axis simultaneously (∆xy), the focal spot quality is sufficiently degraded that no intensity enhancement is achievable.
Figure 4(b) shows the effect of a longitudinal OAP displacement,∆z. A displacement of this type results in the output image position, nominally at f2, being displaced to a new effective best position. Accordingly this misalignment can be characterised in two ways: (1) with the objective lens translated to account for the OAP displacements; and (2) with the objective lens fixed at position f2. The latter case is analogous to an interaction target placed at the nominal focus position and is thus important for practical use of the optic.
When the objective lens is translated, Fig. 4(b) (black data points), the output focal spot quality remains relatively high compared to the other misalignment forms, i.e. ∆x
Encircled Energy in 0.76
m [FWHM] (%)
Encircled Energy in 0.76
m [FWHM] (%)
Objective lens stationary Objective lens correction
0 100 200 300 400 500
0 5 0 5 0 5 0
Figure 4: (a) Plot of the output focus (f2) encircled energy percentage contained within a circle of diameter
equal to the FWHM optimised focal spot (i.e. 0.76µm), as a function of OAP focus displacements from
position f1. Black symbols correspond to∆x; red symbols correspond to∆y; and blue symbols correspond
to∆xy(equal magnitude inxandy) displacements. (b) Same, but for the case where the OAP displacement
is along the input beam direction,∆z. Black symbols corresponds to the case where the objective lens image
plane is adjusted to locate the best focus, i.e. maximised encircled energy, and red symbols correspond to
the case where it remains stationary at the position of optimised alignment focus, i.e f2. In both (a) and (b)
alignment, which consequently helps to optimise the FPM alignment. In the second case, when the objective lens remains fixed at position f2, Fig. 4(b) (red data points), intensity enhancement is only possible for displacements of <30µm, due to fast degradation of the focal spot quality with increase misalignment.
To quantify the magnitude of the longitudinal displacements in the OAP focus posi-tion from nominal (which the FPM is aligned to) which may occur on the Vulcan PW laser, a Shack-Hartmann wavefront sensor was employed to measure the degree of phase aberrations present in the laser wavefront; aberrations which will result in non-ideal focusing from the OAP. This measurement is critical to gauge if the use of a FPM is ben-eficial in terms of intensity enhancement or if shot-to-shot misalignments are too large to achieve enhancement. Fluctuations in the OAP focus position were measured over a series of full energy shots, with average values<20µm observed. The resultant displace-ment from position f2 to the effective best focus, ∆v, as a function of this shift, ∆u, is found to equal∆v =−m2∆u (mbeing the FPM magnification [m=1/3]). This is confirmed both experimentally and by the ray-trace model. A value ∆u=20 µm would therefore yield a 2.2 µm displacement in the output focus position. The consequence of this is that a target aligned to the nominal focus would be irradiated with a pulse with a factor ×2.3 peak intensity reduction (from 3.4×1021to 1.5×1021Wcm−2). This would still result in an intensity enhancement over the direct target irradiation with the F/3.1 OAP. This analysis demonstrates the importance of monitoring the degree of OAP focus position displacement when using a FPM in order to assess its operation and assess the level of intensity enhancement achieved.
Optic Testing in Plasma Operation
The laser-plasma acceleration mechanism utilised is known as target normal sheath ac-celeration (TNSA) . This results from a strong electrostatic field formed at the target rear surface, by fast electrons produced at the front side and transported through the foil. The maximum proton energy achieved via this mechanism is correlated to the peak laser intensity [32,33], via the temperature and density of the fast electrons .
Proton acceleration was achieved using either a FPM or a PPM, both made from the same material (PMMA). The PPM shots were necessary to acquire reference proton en-ergies with the same reflectivity and intensity contrast enhancement to gauge the FPM performance. P-polarised pulses incident at 0° to aluminium target foils with thickness equal to 6µm and transverse dimensions 1 mm ×1 mm were used throughout. Accel-erated protons were detected using a stack of dosimetry (radiochromic, RCF)  film positioned 50 mm behind the target foil centred on the target normal axis. This enables proton energy measurements to be made at discrete energies. Figure5(a)-(b) summarises the results of a series of shots using both plasma mirror types.
A maximum proton energy in the range 24.9 - 53.1 MeV was measured when using the FPMs, and 19.7 - 29.0 MeV was measured for the PPM shots. Comparing the maxi-mum of these ranges, almost a factor of two enhancement was achieved by employing the FPM. This increase occurs with an estimated intensity enhancement factor of×2.6 (from 3.9×1020Wcm−2to 1.0×1021Wcm−2). It should be noted that the intensity achieved using the FPM is lower than predicted from the characterisation study, Fig. 3(a)-(b) (3.4×1021 Wcm−2), due to a lower on-target pulse energy than that used to calculate the predicted value, caused by a lower than expected energy throughput from compressor.
Figure 5: (a) Plot of the measured maximum proton energy, achieved using the FPM, as a function of the
longitudinal displacement measured in the input focal spot position from f1. (b) Plot of the measured
maximum proton energy (Epmax) achieved with both the FPM (red circles) and PPM (black squares), as a
function of the intensity (I) on target, when taking into account the displacement in OAP focus position.
In the PPM cases intensity was varied by changing the pulse energy. The dotted line represents a simple
power fit (of the formEpmax=a.Ib) to show the approximate scaling of the maximum proton energy with
peak laser intensity.
for the reduction in intensity due to misalignment of the OAP focus with respect to the f1 position, the FPM data does not follow the TNSA scaling fit as strongly as the PPM data. This may point to other sources of error affecting the peak intensity achieved - for example in accurately positioning of the target at the focus (f2) of the small F/# beam due to the very small Rayleigh range (∼5.5 µm). This issue will be investigated in more detail in further work.
These test results indicate that the FPM does successfully enhance the intensity when optimally aligned, as indicated by the factor of two increase in maximum proton energy, but that successful operation crucially depends on minimising the displacement of the input focus with respect to position f1.
The design, testing and demonstration of a focusing plasma mirror, based on an el-lipsoidal geometry for demagnification of an ultra-intense laser focal spot, is reported. The design involved optimisation of the incident laser intensity to maximise the plasma reflectivity. The reflected energy on full power shots with the FPM is found to be∼ 15-20% lower than the value predicted in the design (as shown in Fig. 2). This difference will be investigated in detail in future work, together with the effect of adding an AR coating to increase the plasma mirror intensity contrast enhancement factor, enabling investigations utilising sub-micron solid targets.
Direct measurements of the focal spot formed by the FPM using a low-energy laser demonstrated a factor of×2.5 reduction in focal spot size, resulting in an estimated fac-tor of ×3.6 intensity enhancement, when considering the focal spot quality (encircled energy) and the reflectivity. It is found that the optics focal spot quantity is very sensi-tive to misalignments, but when minimised successful FPM operation is achieved. This is demonstrated through the enhancement of maximum proton energies accelerated from foil targets when the optic is optimally aligned.
Due to the limited research performed to date on this type of focusing plasma optic, especially in conjunction with petawatt scale laser systems, the present study helps to bring plasma-based optical technology closer to maturity. Under optimum alignment conditions, a peak intensity of ∼4×1021 Wcm−2 could be achieved when employing the FPM on the Vulcan PW laser system, as determined from the focal spot characterisation. Optimisation of the Vulcan laser to enhance the pulse energy and to decrease the pulse duration, could yield peak intensities close to 1022 Wcm−2 when using the FPM. This would provide a window into the physics achievable with future multi-petawatt laser systems. Focusing plasma mirrors such as the type described here could also be devel-oped for use on these higher power lasers, which would also push the intensity frontier achievable yet further. In the process, this will open up the exploration of new high field physics phenomena at the focus of intense laser pulses.
We acknowledge the expert support of staff at the Central Laser Facility of the Rutherford Appleton Laboratory. This research is financially supported by EPSRC (grants: EP/J003832/1, EP/L001357/1 and EP/K022415/1). Data associated with re-search published in this paper can be accessed at: http://dx.doi.org/10.15129/
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